...ormal step are very reasonable in practice, as it is known that they hold if, for instance, nk is computed by applying one or more steps of a truncated conjugate-gradient method (see Toint, 1981, and =-=Steihaug, 1983-=-) to the minimization of the square of the linearized infeasibility. Note that the conditions (2.3), (2.4) and (2.5) allow us to choose a null normal step (nk = 0) if xk is feasible. Having computed t...

... preliminary numerical experience discussed in the next section has shown that our algorithm, like many SQP methods, might suffer from the Maratos effect. A well documented cure for this problem (see =-=Mayne and Polak, 1982-=-, Coleman and Conn, 1982, or Section 15.3.2 of Conn et al., 2000) is to use second-order correction steps. In our context, we define a such a step sC k as a step performed from xk + sk to correct for ...

...experience discussed in the next section has shown that our algorithm, like many SQP methods, might suffer from the Maratos effect. A well documented cure for this problem (see Mayne and Polak, 1982, =-=Coleman and Conn, 1982-=-, or Section 15.3.2 of Conn et al., 2000) is to use second-order correction steps. In our context, we define a such a step sC k as a step performed from xk + sk to correct for an unsuccessful f-iterat...

... (1995), El-Alem (1995, 1999), Byrd, Gilbert and Nocedal (2000a), Byrd, Hribar and Nocedal (2000b), Liu and Yuan (2000) and Lalee, Nocedal and Plantenga (1998) (also see Chapter 15 of Conn, Gould and =-=Toint, 2000-=-). The algorithm presented here has four main features. The first is that it attempts to consider the objective function and the constraints as independently as possible by using different models and ...